This study extends the imaging, magnification, and aberration properties of the images formed from holograms to the nonparaxial case. This extension yields expressions which can be used to locate accurately the position of an image point in those cases where the paraxial theory fails. The readout-illumination critical angles for image formation are predicted and related to the critical angles of a diffraction grating. The ratio of readout wavelength to recording wavelength is limited, and consequently wavelength-change magnification is limited, for certain types of holograms. The expressions developed are kept in the same form as those developed for the paraxial case so that the reduction to the paraxial case is obvious, and the many prior comments made on aberration reduction are applicable by a simple change of variable.
© 1967 Optical Society of America
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